Lump interaction phenomena to the nonlinear ill-posed Boussinesq dynamical wave equation

Abstract

In this manuscript, we discuss the dynamical behavior of ill-posed Boussinesq (IPB) dynamical wave equation. This equation depicts how long wave made in shallow water propagates due to the influence of gravity. The different wave structures are extracted by the utilization of Hirota's bilinear method (HBM) and different test function approaches. The wave structures in the forms of novel breather waves, lump solutions, two-wave solutions, and rogue wave solutions are obtained. Furthermore, with assistance of appropriate parameters, the acquired solutions' physical behavior is drawn out in 3 dimensional, and contour profiles. As a consequence of the obtained results, we can claim that the used methodology is simple, dynamic, extremely effective, and will serve as a useful tool for solving more severely nonlinear problems in a variety of domains, most notably ocean and coastal engineering. Additionally, our findings provide an important first step in comprehending the structure and physical behavior of complex structures. We hope that our findings will contribute significantly to our understanding of ocean waves. This work, we believe, is timely and will be of interest to a broad range of professionals involved in ocean engineering models. The obtained results are useful in grasping the fundamental scenarios of nonlinear sciences. With the help of Mathematica, the obtained results are verified by inserting them into the governing equation.